Speed Maths: Multiplication Shortcuts for Aptitude Tests

Speed-multiplication shortcuts reduce calculation time from around 30 seconds to under 5 for most aptitude question types. Six methods below cover the multipliers that appear most often in Indian placement tests, and every example is verified by direct multiplication.

The legacy article this piece replaces had carried arithmetic errors in the slide-and-add section. Every carry chain here is spelled out fully so you can audit each step.

Why Calculation Speed Matters in Placement Tests

The TCS NQT Numerical Ability section and AMCAT Quantitative Aptitude both run under strict time limits. The difficulty is not that the problems are hard; it is that they require multi-step calculations inside a tight window. A candidate doing mental arithmetic in 5 seconds rather than 30 has roughly 25 extra seconds per question, which adds up to a substantial buffer across a full section.

Speed maths is not about memorising extended multiplication tables. It is about rewriting the problem into a form where the arithmetic is simple: powers of 10 are trivial to handle, small corrections are trivial to add or subtract, and the slide-and-add pattern for 11 removes long multiplication entirely.

For similar pattern-matching shortcuts applied to time-based questions, the article on solving questions on clocks for competitive exams uses the same decomposition principle in a different topic domain.

Powers-of-10 Shortcuts: Multiply by 5, 25, 75, and 125

These four tricks share one idea: rewrite the multiplier as a fraction with a power of 10 in the numerator. Divide the base number first, then shift the decimal.

Multiply by 5

Since 5 = 10 / 2, divide by 2 and multiply by 10.

• Example: 4,386 x 5
• Step 1: 4,386 / 2 = 2,193
• Step 2: 2,193 x 10 = 21,930
• Direct verify: (4,000 + 386) x 5 = 20,000 + 1,930 = 21,930 ✓

Multiply by 25

Since 25 = 100 / 4, divide by 4 and multiply by 100.

• Example: 4,386 x 25
• Step 1: 4,386 / 4 = 1,096.5
• Step 2: 1,096.5 x 100 = 109,650
• Direct verify: 4,386 x 100 / 4 = 438,600 / 4 = 109,650 ✓

If the number is not divisible by 4, the decimal .5 from dividing by 4 becomes .0 after the x 100 shift, so the final answer is always a whole number.

Multiply by 75

Since 75 = 300 / 4, divide by 4 and multiply by 300.

• Example: 48 x 75

• Step 1: 48 / 4 = 12

• Step 2: 12 x 300 = 3,600

• Direct verify: 48 x 25 x 3 = 1,200 x 3 = 3,600 ✓

• Second example: 72 x 75

• Step 1: 72 / 4 = 18

• Step 2: 18 x 300 = 5,400

• Direct verify: 72 x 25 x 3 = 1,800 x 3 = 5,400 ✓

Multiply by 125

Since 125 = 1000 / 8, divide by 8 and multiply by 1000.

• Example: 8,672 x 125

• Step 1: 8,672 / 8 = 1,084 (8,000 / 8 = 1,000; 672 / 8 = 84; total 1,084)

• Step 2: 1,084 x 1,000 = 1,084,000

• Direct verify: 8,672 x 125 = 1,084,000 ✓

• Second example: 248 x 125

• Step 1: 248 / 8 = 31

• Step 2: 31 x 1,000 = 31,000

• Direct verify: 248 x 1,000 / 8 = 248,000 / 8 = 31,000 ✓

Anchoring Near-100 Multipliers: 98, 99, 101, and 102

When a multiplier sits close to 100, express it as 100 ± n. One multiplication by 100 (append two zeros), then one small correction of size n.

Multiply by 98

Since 98 = 100 - 2, multiply by 100 and subtract 2 times the base.

• Example: 864 x 98
• Step 1: 864 x 100 = 86,400
• Step 2: 864 x 2 = 1,728
• Step 3: 86,400 - 1,728 = 84,672
• Carry-chain verify: 86,400 - 1,000 = 85,400; minus 700 = 84,700; minus 28 = 84,672 ✓

Multiply by 99

Since 99 = 100 - 1, multiply by 100 and subtract the base once.

• Example: 47 x 99
• Step 1: 47 x 100 = 4,700
• Step 2: 4,700 - 47 = 4,653
• Direct verify: 47 x (100 - 1) = 4,700 - 47 = 4,653 ✓

Multiply by 102

Since 102 = 100 + 2, multiply by 100 and add 2 times the base.

• Example: 864 x 102
• Step 1: 864 x 100 = 86,400
• Step 2: 864 x 2 = 1,728
• Step 3: 86,400 + 1,728 = 88,128
• Direct verify: 864 x 100 + 864 x 2 = 86,400 + 1,728 = 88,128 ✓

The pattern extends naturally: for 97 = 100 - 3, multiply by 100 and subtract 3 times the base.

The Slide-and-Add Method for Multiplying by 11

This is the most elegant trick in the set and the most likely source of errors under exam pressure. Carry chains are where candidates drop marks.

Algebraic derivation

For a two-digit number with tens digit a and units digit b, multiplying by 11 gives:

ab x 11 = ab x (10 + 1) = ab x 10 + ab x 1

Adding these two terms column by column:

• Ones position: b
• Tens position: a + b (carry 1 leftward if this sum exceeds 9)
• Hundreds position: a plus any carry

The result has the pattern a | (a+b) | b, with carries propagated left whenever a sum crosses 9.

Two-digit examples with full carry chains

Without carry: 54 x 11

• Ones: 4
• Tens: 5 + 4 = 9 (no carry)
• Hundreds: 5
• Result: 5 | 9 | 4 = 594
• Direct verify: 540 + 54 = 594 ✓

With carry: 78 x 11

• Ones: 8
• Tens: 7 + 8 = 15; write 5, carry 1
• Hundreds: 7 + 1 (carry) = 8
• Result: 8 | 5 | 8 = 858
• Direct verify: 780 + 78 = 858 ✓

Three-digit number with two carries: 476 x 11

For a three-digit number with digits a, b, c, the raw positions before carrying are a | (a+b) | (b+c) | c.

• a = 4, b = 7, c = 6
• Raw: 4 | 11 | 13 | 6
• Carry chain (right to left):
  • Ones position: 6, no carry
  • Tens position: 13; write 3, carry 1
  • Hundreds position: 11 + 1 (carry) = 12; write 2, carry 1
  • Thousands position: 4 + 1 (carry) = 5
• Result: 5 | 2 | 3 | 6 = 5,236
• Direct verify: 4,760 + 476 = 5,236 ✓

Without carry: 352 x 11

• Raw: 3 | (3+5) | (5+2) | 2 = 3 | 8 | 7 | 2 = 3,872
• Direct verify: 3,520 + 352 = 3,872 ✓

For the extension to multiplying any number by 111, the multiplying a number with 111 article applies the same sliding logic to a three-digit multiplier, including the longer carry chains it produces.

Putting the Tricks Together

The decision rule for choosing a shortcut:

• Multiplier is 5, 25, 75, or 125: use powers-of-10 substitution.
• Multiplier is 97 through 103: use near-100 anchoring.
• Multiplier is 11, 111, or 1,111: use the slide-and-add rule.

Practise each method with 10 isolated problems before mixing them. Mixing all six in a first session consistently produces carry-chain errors in the x11 method; isolated repetition builds the pattern first.

The calendar aptitude section applies a closely related shortcut approach: break the problem into independent components, handle each part in a step, combine at the end. The underlying skill is identical to what these multiplication tricks train.

After aptitude clears the first screening round, product and tech roles often include an AI-literacy check. The same decompose-then-recombine logic that turns a four-digit multiplication into two mental steps is also the right model for how large language models break text into tokens and generate responses. TinkerLLM at ₹299 covers that second tier, from prompt structure to RAG patterns, at a density comparable to how these multiplication tricks scale through an aptitude section.